“Now here we are, 10 years later,” Durbin said. “If you asked me if I was signing up for the longest war in U.S. history, with no end in sight, even with the killing of Osama bin Laden, that was not the bargain, that is not what I was signing up for.”

While Levin has no plans to push legislation requiring such a pullout, he will publicly advocate for a “significant reduction,” he said Monday.

The White House has stressed that the death of bin Laden is a major victory in the battle against al Qaeda, but should not be seen as a reason to change the U.S. game plan in Afghanistan.

White House press secretary Jay Carney said Tuesday that Obama’s strategy for Afghanistan and Pakistan “remains very much in place.”

Carney said the president is committed to the war in Afghanistan, and that the pace of a troop drawdown will “be determined by the conditions on the ground.”

Carney said the president is still focused on pursuing and destroying the al Qaeda network, and that will continue in the way Obama laid out when he unveiled his plan for the region in December 2009. “Getting bin Laden was very much a part of that plan, but it was not the only part,” he said.

A weariness about the Afghanistan war had set in well before bin Laden’s killing. A March poll by ABC News and The Washington Post found that nearly two-thirds of those responding no longer think the war is worth fighting.

A new poll released Wednesday by Gallup found more than 50 percent of Americans still think the country has work to do in Afghanistan, but also revealed a significant party split.

Fifty-four percent of Democrats said the U.S. had achieved its goal in Afghanistan, compared to 38 percent of Republicans and 44 percent of independents.

On Capitol Hill, many lawmakers are worried not only about those polls, but about the cost of continuing the war at a time of record deficits. The fact that recent attempted attacks on U.S. soil have been hatched in other countries also has raised questions about continuing the fight in Afghanistan.

During a Senate Foreign Relations Committee hearing on Tuesday, several committee members zeroed in on the tens of billions of dollars Washington already has spent in Afghanistan, and questioned whether such expenditures are sustainable in the future.

Sen. Dick Lugar (R-Ind.), the panel’s ranking member, said Afghanistan no longer holds the strategic importance to match Washington’s investment. He cited recent comments from senior national-security officials that terrorist strikes on America are more likely to be planned in places like Yemen.

He said it is no longer “clear why we’re there,” saying nations like Yemen that harbor extremists “are getting a free pass.”

Lugar raised concerns that U.S. policy on Afghanistan is focused more on building up its economic, political and security systems. “Such grand nation-building is beyond our powers,” he said bluntly.

Lugar called on Obama to define success in Afghanistan, and to begin working toward that revised goal.

There remains a level of support for the fight in Afghanistan in both parties, and bin Laden’s death has not led to a groundswell of calls for troop withdrawals.

“As we debate the end-state, we must factor in what we can afford in light of our budget constraints,” the chairman said. “We will spend $120 billion in Afghanistan this fiscal year, and our decisions on resource allocations there affect our global posture elsewhere, as we see today in the Middle East. We have to ask at every turn if our strategy in Afghanistan is sustainable.”

While lawmakers appear willing to see what happens in Afghanistan over the next few months, some, like Corker, are asking pointed questions about whether Washington can replicate this kind of mission elsewhere.

“This is not a model for the future,” Corker said. “This is not something we can do in country after country after country.”

Sam Youngman and Shane D'Aprile contributed.

This story was first posted at 8:05 p.m. May 3 and updated at 9:11 a.m. May 4.